ot.Log.Show(ot.Log.NONE) # %% # Define the coefficients distribution mu = [2.0]*2 sigma = [5.0]*2 R = ot.CorrelationMatrix(2) coefDist = ot.Normal(mu, sigma, R) # %% # Create a basis of functions phi_1 = ot.SymbolicFunction(['t'], ['sin(t)']) phi_2 = ot.SymbolicFunction(['t'], ['cos(t)^2']) myBasis = ot.Basis([phi_1, phi_2]) # %% # Create the mesh myMesh = ot.RegularGrid(0.0, 0.1, 100) # %% # Create the process process = ot.FunctionalBasisProcess(coefDist, myBasis, myMesh) # %% # Draw a sample N = 6 sample = process.getSample(N) graph = sample.drawMarginal(0) graph.setTitle(str(N)+' realizations of functional basis process') view = viewer.View(graph)
def _exec(self, X):
Xs = ot.Sample(X)
x1, x2, x3, x4 = Xs.computeMean()
y = x1 + x2 + x3 - x4 + x1 * x2 - x3 * x4 - 0.1 * x1 * x2 * x3
return [y]
f = ot.FieldToPointFunction(pyf2p(tg))
# First process: elementary process based on a bivariate random vector
f1 = ot.SymbolicFunction(['t'], ['sin(t)'])
f2 = ot.SymbolicFunction(['t'], ['cos(t)^2'])
myBasis = ot.Basis([f1, f2])
coefDis = ot.Normal([1.0] * 2, [0.6] * 2, ot.CorrelationMatrix(2))
p1 = ot.FunctionalBasisProcess(coefDis, myBasis, tg)
# Second process: smooth Gaussian process
p2 = ot.GaussianProcess(ot.SquaredExponential([1.0], [T / 4.0]), tg)
# Third process: elementary process based on a bivariate random vector
randomParameters = ot.ComposedDistribution([ot.Uniform(), ot.Normal()])
p3 = ot.FunctionalBasisProcess(
randomParameters,
ot.Basis([
ot.SymbolicFunction(["t"], ["1", "0"]),
ot.SymbolicFunction(["t"], ["0", "1"])
]))
X = ot.AggregatedProcess([p1, p2, p3])
X.setMesh(tg)
#
# %%
import openturns as ot
from openturns.viewer import View
# %%
# First build a process to generate the input data.
# We assemble a 4-d process from functional and Gaussian processes.
T = 3.0
NT = 32
tg = ot.RegularGrid(0.0, T / NT, NT)
f1 = ot.SymbolicFunction(['t'], ['sin(t)'])
f2 = ot.SymbolicFunction(['t'], ['cos(t)^2'])
coeff1_dist = ot.Normal([1.0] * 2, [0.6] * 2, ot.CorrelationMatrix(2))
p1 = ot.FunctionalBasisProcess(coeff1_dist, ot.Basis([f1, f2]), tg)
p2 = ot.GaussianProcess(ot.SquaredExponential([1.0], [T / 4.0]), tg)
coeff3_dist = ot.ComposedDistribution([ot.Uniform(), ot.Normal()])
f1 = ot.SymbolicFunction(["t"], ["1", "0"])
f2 = ot.SymbolicFunction(["t"], ["0", "1"])
p3 = ot.FunctionalBasisProcess(coeff3_dist, ot.Basis([f1, f2]))
X = ot.AggregatedProcess([p1, p2, p3])
X.setMesh(tg)
# %%
# Draw some input trajectories from our process
ot.RandomGenerator.SetSeed(0)
x = X.getSample(10)
graph = x.drawMarginal(0)
graph.setTitle(f'{x.getSize()} input trajectories')
_ = View(graph)
import openturns as ot
from math import exp
from matplotlib import pyplot as plt
from openturns.viewer import View
f1 = ot.SymbolicFunction(['t'], ['sin(t)'])
f2 = ot.SymbolicFunction(['t'], ['cos(t)*cos(t)'])
myBasis = ot.Basis([f1, f2])
coefDis = ot.Normal([2] * 2, [5] * 2, ot.CorrelationMatrix(2))
myTG = ot.RegularGrid(0.0, 0.1, 250)
myFBP = ot.FunctionalBasisProcess(coefDis, myBasis, myTG)
TS = myFBP.getRealization()
graph = TS.draw()
graph.add(myFBP.getRealization().draw())
graph.add(myFBP.getRealization().draw())
graph.setColors(['red', 'blue', 'green'])
fig = plt.figure(figsize=(10, 4))
plt.suptitle('Functional Basis Process')
fbp_axis = fig.add_subplot(111)
view = View(graph, figure=fig, axes=[fbp_axis], add_legend=False)